We went to a taping of Jeopardy and The Tonight Show. They were both pretty interesting. I wanted to see Raymond but it wasn't available that week.
You can walk on the beach and watch the planes fly into LAX. Go down and eat seafood along the boardwalk area.
Did lots of hiking in mountain/canyon parks in the Hollywood Hills area.
The Gene Autry Western Museum was fun--especially for my husband who's a cowboy and western movie fan.
I enjoyed a Hispanic type market in the downtown area of LA. Can't remember the name but it had some great places to eat and lots of spices, candy, dried nuts, fruit and other food items unusual to where I live.
We visited a Thai temple on a Sunday and participated in the food fair conducted by ladies of the temple. The people were friendly and nice. Sweet Willie had posted about this under the food section and it was great.
We also visited Marilyn Monroe's mausoleum as this is something I'd read about since I was child.
Also, I second the Getty. It was great and what a location.